CN117556677B

CN117556677B - Section bar die optimization method and system based on multi-objective optimization algorithm

Info

Publication number: CN117556677B
Application number: CN202410043562.8A
Authority: CN
Inventors: 姜锋; 许栩达; 吴飞飞; 蒋春丽
Original assignee: Central South University
Current assignee: Central South University
Priority date: 2024-01-11
Filing date: 2024-01-11
Publication date: 2024-03-26
Anticipated expiration: 2044-01-11
Also published as: CN117556677A

Abstract

The invention provides a section bar die optimization method and a section bar die optimization system based on a multi-objective optimization algorithm, wherein the method comprises the following steps: obtaining a die structure parameter of a target die to be optimized and a profile parameter of a target profile produced by using the target die; determining and optimizing a thermal deformation constitutive model of the target profile based on profile parameters; performing section molding finite element simulation on the target die according to the thermal deformation constitutive model, and determining a plurality of optimization variable indexes and optimization targets; obtaining an influence relation between the mould structure parameter and a plurality of optimization variable indexes through response surface analysis, and constructing a parameter relation model between the mould structure parameter and the plurality of optimization variable indexes; performing multi-objective optimization on the parameter relation model by using an NSGA2 algorithm based on the optimization targets to obtain an optimized final solution for achieving all the optimization targets; and optimizing and adjusting the structural parameters of the die through optimizing the final solution. The invention can play an effective die optimizing effect through multi-objective optimization.

Description

Section bar die optimization method and system based on multi-objective optimization algorithm

Technical Field

The invention belongs to the technical field of mold design, and particularly relates to a section mold optimization method and system based on a multi-objective optimization algorithm.

Background

The extrusion die is a critical tool in aluminum profile production, and die design optimization is a key method for prolonging the service life of the die and eliminating profile production quality abnormality. However, current criteria for die optimization effect focus on single-objective optimization based on profile section flow variance (SDV). With the rapid change of the market, especially the wide application of new energy automobiles to section bars, some new technical characteristics appear. For example, the side beam section bar in the new energy automobile battery tray component has the characteristics of a plurality of cavities, large wall thickness deviation and concentrated local mass.

Compared with the traditional profile structure, the boundary beam profile in the new energy automobile battery tray assembly has large hydrostatic pressure difference on two sides of the die core head due to large wall thickness difference, so that the core head is offset towards the low pressure side (thick wall position), the dimension of the profile is possibly caused to exceed the standard, even irreversible plastic deformation of the core head occurs, and adverse effects are generated on the product quality and the service life of the die. On the other hand, the offset of the core print may also form a blockage or flow promotion angle, resulting in a profile cross-sectional flow rate that is more difficult to control, exacerbating the deterioration of the SDV indicator. In addition, because the mass distribution is uneven, the parts with concentrated mass possibly cause difficult filling of the section bar due to insufficient hydrostatic pressure, and loose or hollow holes are generated, so that serious potential safety hazards are brought to subsequent processing and use. Therefore, for a multi-cavity profile with large wall thickness difference, if only a single optimization target such as a section flow velocity variance (SDV) is considered in the profile die optimization process of the profile, the optimization effect of the profile die is difficult to achieve, and the profile processed and produced by using the optimized die is difficult to meet the profile quality requirement.

Disclosure of Invention

The invention provides a section mould optimization method and system based on a multi-objective optimization algorithm, which are used for solving the problem that in the optimization process of a section mould with multiple cavities and large wall thickness difference, only a single optimization objective is considered, so that an optimization effect is difficult to achieve.

In a first aspect, the present invention provides a profile mold optimization method based on a multi-objective optimization algorithm, the method comprising the steps of:

obtaining a die structure parameter of a target die to be optimized and a profile parameter of a target profile produced by using the target die, wherein the target profile comprises a cavity part, a thin-wall part and a thick-wall part;

determining and optimizing a thermal deformation constitutive model of the target profile based on the profile parameters;

performing section molding finite element simulation on the target die according to the thermal deformation constitutive model, and determining a plurality of optimization variable indexes of the target die and optimization targets of the optimization variable indexes;

obtaining an influence relation between the mould structure parameter and a plurality of optimized variable indexes through response surface analysis, and constructing a parameter relation model between the mould structure parameter and the optimized variable indexes by combining the influence relation with the optimized target;

Performing multi-objective optimization on the parameter relation model based on the optimization objective and by utilizing a rapid non-dominant sorting algorithm with elite retention strategy to obtain an optimized final solution for achieving all the optimization objectives;

and optimizing and adjusting the structural parameters of the die through the optimized final solution.

Optionally, the profile parameters include a plurality of sets of test temperatures and a plurality of sets of test strain parameters, and the determining and optimizing the thermal deformation constitutive model of the target profile based on the profile parameters includes the following steps:

generating a standard thermal deformation constitutive model according to a preset alloy database, wherein the standard thermal deformation constitutive model comprises standard material parameters;

carrying out multiple hot compression tests by combining multiple groups of test temperatures and multiple groups of test strain parameters, and calculating all test results by adopting a linear fitting method to obtain optimal material parameters;

and replacing the standard material parameters in the standard thermal deformation constitutive model with the optimal material parameters to obtain the thermal deformation constitutive model of the target profile.

Optionally, the test strain parameters include a test strain force, a test strain amount and a test strain rate, and the expression of the thermal deformation constitutive model of the target profile is as follows:

Wherein:representing the test strain force,/->Representing the test strain amount,/->Representing the test strain rate,/->Indicating the test temperature, +.>Are different said optimal material parameters.

Optionally, the performing the finite element modeling on the target mold according to the thermal deformation constitutive model, and determining a plurality of optimization variable indexes of the target mold and optimization targets of the optimization variable indexes respectively includes the following steps:

arranging a plurality of first measuring points along the length direction of the target die in the cavity part;

providing a plurality of second measuring points on the thick-wall part around the geometric center of the thick-wall part;

performing section molding finite element simulation on the target die according to the thermal deformation constitutive model;

detecting fluid flow rates of a plurality of first measuring points in the section molding finite element simulation process, and calculating a flow standard deviation based on all the fluid flow rates to obtain the flow standard deviation as an optimized variable index of the target die;

detecting fluid pressure of a plurality of first measuring points in the section molding finite element simulation process, and calculating pressure standard deviation based on all the fluid pressure to obtain the pressure standard deviation as the optimized variable index;

Detecting fluid pressure of a plurality of second measuring points in the section molding finite element simulation process, and calculating thick-wall hydrostatic pressure based on all the fluid pressure to serve as the optimization variable index;

and combining the molding change of the profile in the process of modeling the profile finite element for a plurality of times, and determining the standard deviation of the flow rate, the standard deviation of the pressure and the optimization target of the thick-wall hydrostatic pressure.

Optionally, the die structure parameters include a material blocking table height, a working belt length and a false core head height, and before the influence relation between the die structure parameters and the plurality of optimized variable indexes is obtained through response surface analysis, the parameter relation model between the die structure parameters and the plurality of optimized variable indexes is constructed by combining the influence relation and the optimized targets, the method further includes the following steps:

combining the mould structure parameters and a plurality of the optimized variable indexes, and carrying out finite element simulation analysis according to the effect surface method test design to obtain a plurality of parameter relations between the mould structure parameters and the plurality of the optimized variable indexes;

constructing a ternary quadratic regression model based on various parameter relationships by adopting a stepwise regression method, wherein the ternary quadratic regression model comprises a flow rate standard deviation regression model, a pressure standard deviation regression model and a thick-wall hydrostatic pressure regression model;

And verifying that the structural parameters of the die belong to the influence factors of the optimized variable indexes by carrying out P value inspection on the ternary quadratic regression model.

Optionally, the obtaining the influence relation between the mold structural parameter and the plurality of optimized variable indexes through response surface analysis, and constructing a parameter relation model between the mold structural parameter and the plurality of optimized variable indexes by combining the influence relation and the optimized target, includes the following steps:

sequentially taking the standard deviation of the flow rate, the standard deviation of the pressure and the hydrostatic pressure of the thick wall as response targets, and taking any two of the structural parameters of the die as influence factors to generate a plurality of second-order response curved surfaces;

analyzing all the second-order response curved surfaces to determine the influence relation between the structural parameters of the die and a plurality of optimized variable indexes;

and constructing a parameter relation model between the structural parameters of the mould and a plurality of optimized variable indexes based on the ternary quadratic regression model and combining the influence relation and the optimized targets.

Optionally, the multi-objective optimization is performed on the parameter relation model based on the optimization objective and by using a fast non-dominant sorting algorithm with elite retention policy, and the obtaining an optimized final solution for achieving all the optimization objectives includes the following steps:

Performing multi-objective optimization on the parameter relation model based on the optimization targets and by utilizing a rapid non-dominant sorting algorithm with elite retention strategy to obtain Pareto optimal solution sets of all the optimization targets;

taking all the optimization targets as evaluation indexes, and generating an index matrix based on the Pareto optimal solution set;

normalizing the index matrix;

weighting each element in the index matrix by utilizing index weights preset by the evaluation index to obtain a weighting matrix;

and evaluating and sequencing all solutions in the Pareto optimal solution set by adopting a TOPSIS method based on the weighting matrix, and finally obtaining an optimal final solution which achieves all the optimal targets and belongs to an optimal level in the Pareto optimal solution set.

Optionally, the multi-objective optimization is performed on the parameter relation model based on the optimization objective and by using a fast non-dominant sorting algorithm with elite retention policy, and obtaining Pareto optimal solution sets of all the optimization objectives includes the following steps:

randomly generating an original population based on the parametric relationship model;

and carrying out repeated iterative evolutionary operation on the original population by using a rapid non-dominant sorting algorithm with elite retention strategy until the number of iterations reaches a preset algebraic threshold, wherein the repeated iterative evolutionary operation comprises the following steps:

Calculating a target value of each individual in the original population according to the optimization target;

calculating the crowding distance of the original population based on the target numerical value, and performing a rapid non-dominant sorting operation on the original population according to the crowding distance to screen out part of individuals in the original population;

selecting the rest individuals in the original population to obtain a basic population;

performing cross mutation operation on the basic population by combining preset cross probability and preset mutation probability to obtain a new generation population, and combining the new generation population and the original population into an original population for the next iteration evolution;

and taking the target value of each individual in the new generation population of the last round of iterative evolution as a Pareto optimal solution set of all the optimization targets.

Optionally, the estimating and sorting the solutions in the Pareto optimal solution set based on the weighting matrix and using a TOPSIS method, and finally obtaining an optimal final solution in the Pareto optimal solution set, which achieves all the optimization targets and belongs to an optimal level, includes the following steps:

taking the minimum element of each column in the weighting matrix as an optimal solution, and taking the maximum element of each column in the weighting matrix as a worst solution;

Respectively calculating Euclidean distances between each element in the weighting matrix and the optimal solution and the worst solution;

calculating the proximity index of each element in the weighting matrix and the optimal level according to the Euclidean distance;

and performing descending order sorting on the proximity indexes, and selecting an element at the first bit of the sorting order as an optimized final solution which achieves all the optimization targets and belongs to the optimal level in the Pareto optimal solution set.

In a second aspect, the present invention also provides a profile mould optimization system based on a multi-objective optimization algorithm, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the profile mould optimization method based on the multi-objective optimization algorithm as described in the first aspect when executing the computer program.

The beneficial effects of the invention are as follows:

the invention can carry out multi-objective optimization for a complex multi-cavity profile mould with large wall thickness difference, specifically, firstly, a plurality of optimization variable indexes of the objective mould and optimization objectives of all the optimization variable indexes are determined through finite element simulation of profile molding, and then, a functional relation between the mould structure parameters of the objective mould and the plurality of optimization variable indexes is obtained through response surface analysis, so that a parameter relation model is constructed. Meanwhile, in order to improve the accuracy of the functional relation and the authenticity of the simulation process, the thermal deformation constitutive model of the target profile is considered and optimized. And finally, calculating a parameter relation model of the nonlinear function formula through an NSGA2 multi-objective genetic optimization algorithm to obtain an optimized final solution, optimizing and adjusting the structural parameters of the die through the optimized final solution, and completing die manufacturing according to the optimized result. Because more key mold structural parameters exist in the complex multi-cavity large-wall-thickness profile mold, compared with the process of optimizing the mold by adopting a single optimization target, the multi-target optimization can obtain an optimal combination scheme of the key mold structural parameters, so that the optimized mold can simultaneously meet a plurality of index requirements when being applied to the profile processing process, and the finally processed profile can also meet the quality requirements.

Drawings

Fig. 1 is a schematic flow chart of a section mould optimizing method based on a multi-objective optimizing algorithm in the invention.

Fig. 2 is a schematic view of a three-dimensional model of a target profile in the present invention.

Fig. 3 is a schematic cross-sectional view of a target profile according to the present invention.

Fig. 4 is a schematic diagram of a process of performing a finite element simulation of profile molding of a target mold in the present invention.

FIG. 5 is a schematic representation of a second order response surface generated in the present invention using the standard deviation of flow rate as the response target and the length of the operating band and the height of the false core as the influencing factors.

FIG. 6 is a schematic diagram of a second order response surface generated in the present invention using the standard deviation of flow rate as a response target and the height of the dam cap and the height of the dummy head as influence factors.

FIG. 7 is a schematic diagram of a second order response surface generated in the present invention using the standard deviation of pressure as a response target and the height of the dam cap and the height of the dummy head as influence factors.

FIG. 8 is a schematic diagram of a second order response surface generated in the present invention using thick wall hydrostatic pressure as a response target and using dam cap height and false core head height as influencing factors.

Fig. 9 is a visual schematic diagram of Pareto optimal solution set in the present invention.

Detailed Description

The terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged, as appropriate, such that embodiments of the present invention may be implemented in sequences other than those illustrated or described herein, and that the objects identified by "first," "second," etc. are generally of a type, and are not limited to the number of objects, such as the first object may be one or more. Furthermore, in the description and claims, "and/or" means at least one of the connected objects, and the character "/", generally means that the associated object is an "or" relationship.

The invention discloses a section bar die optimization method based on a multi-objective optimization algorithm. The technical solutions of the embodiments of the present invention will be clearly described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which are obtained by a person skilled in the art based on the embodiments of the present invention, fall within the scope of protection of the present invention. Referring to fig. 1, the section mould optimization method based on the multi-objective optimization algorithm specifically comprises the following steps:

s101, obtaining the die structure parameters of a target die to be optimized and the profile parameters of a target profile produced by using the target die.

With reference to fig. 2 and 3, an example of the target profile may be a side beam profile in a new energy automobile battery tray assembly. As shown in fig. 3, it can be seen from the sectional view of the profile, the profile includes a thin-wall portion, a thick-wall portion and a plurality of cavity portions, taking the dashed-line frame portion of the profile in fig. 3 as an example, the portion indicated by the area a is the thick-wall portion of the profile, the portion indicated by the area B is the thin-wall portion of the profile, and the position indicated by the area C is one of the cavity portions of the profile. The area of the thick-wall part A is 426mm2 through measurement, the area of the thin-wall part B is 42mm2 through measurement, the difference of the two areas is approximately 10 times, the size of the core head of the cavity part C is smaller, the rigidity of the core head is smaller, the deformation of the core head caused by the material flow velocity difference and the superposition pressure difference on two sides of the core head influences the discharging flow velocity difference and the pressure balance of the section of the whole section, and in the process of die design adjustment, the structural change easily causes the abnormal quality such as cavity, looseness and the like of the thick-wall part A.

S102, determining and optimizing a thermal deformation constitutive model of the target profile based on profile parameters.

The reasonable thermal deformation constitutive model is important to accurately describe deformation behaviors of materials of the target profile under high temperature, large strain and high strain rate. At the same time, the compositional differences between alloys result in significant differences in flow deformation behavior even between alloys of the same family. Therefore, in order to ensure the accuracy of the follow-up section molding finite element simulation, the thermal deformation constitutive model of the target section is also required to be optimized according to the section parameters.

S103, performing finite element simulation on the profile molding of the target die according to the thermal deformation constitutive model, and determining a plurality of optimization variable indexes of the target die and optimization targets of all the optimization variable indexes.

Referring to fig. 4, fig. 4 is a three-dimensional model of a target mold, and the step shown in fig. 4 is a step of dividing a processing grid before finite element simulation of profile molding. The factors influencing the molding quality of the profile are determined through the finite element simulation of the profile molding, a plurality of optimization variable indexes of the target die and the optimization targets of the indexes are further determined according to the factors, and in the optimization process of the target die, the optimization variable indexes are optimized towards the direction of the optimization targets, so that the profile molded by the optimized die has better molding quality.

S104, obtaining an influence relation between the mold structure parameter and a plurality of optimization variable indexes through response surface analysis, and constructing a parameter relation model between the mold structure parameter and the plurality of optimization variable indexes by combining the influence relation and the optimization target.

The response surface method (response surface methodology, RSM) is an optimization method for obtaining a set of optimal design variables by fitting a response surface according to sample data obtained by a set of experiments, giving a surface equation and then solving the surface equation. Compared with other data statistical methods, the RSM not only considers interaction between independent variables and improves fitting precision, but also can display functional relation between the independent variables by using a graphic technology, so that a result is more visual.

S105, performing multi-objective optimization on the parameter relation model based on the optimization targets and by utilizing a rapid Non-dominant ordering (Non-dominated Sorting Genetic Algorithm II, NSGA 2) algorithm with elite retention strategy, so as to obtain an optimized final solution for achieving all the optimization targets.

The optimization variable indexes have independence and have certain internal relation, so that a certain target is found to be improved to the greatest extent under the condition of not sacrificing other targets, the optimization variable indexes belong to the Pareto optimal solution set solving problem, and a rapid Non-dominant sorting (Non-dominated Sorting Genetic Algorithm II, NSGA 2) algorithm with elite retention strategy can be adopted for solving.

S106, optimizing and adjusting the structural parameters of the die through optimizing the final solution.

The implementation principle of the embodiment is as follows:

firstly, determining a plurality of optimization variable indexes and optimization targets of all the optimization variable indexes of a target die through section molding finite element simulation, and then obtaining a functional relation between a die structure parameter of the target die and the plurality of optimization variable indexes through response surface analysis, so as to construct a parameter relation model. Meanwhile, in order to improve the accuracy of the functional relation and the authenticity of the simulation process, the thermal deformation constitutive model of the target profile is considered and optimized. And finally, calculating a parameter relation model of the nonlinear function formula through an NSGA2 multi-objective genetic optimization algorithm to obtain an optimized final solution, optimizing and adjusting the structural parameters of the die through the optimized final solution, and completing die manufacturing according to the optimized result. Because more key mold structural parameters exist in the complex multi-cavity large-wall-thickness profile mold, compared with the process of optimizing the mold by adopting a single optimization target, the multi-target optimization can obtain an optimal combination scheme of the key mold structural parameters, so that the optimized mold can simultaneously meet a plurality of index requirements when being applied to the profile processing process, and the finally processed profile can also meet the quality requirements.

In one embodiment, the profile parameters include a plurality of sets of test temperatures and a plurality of sets of test strain parameters, and step S102 specifically includes the steps of:

In this embodiment, the standard thermal deformation constitutive model is generated according to a preset alloy database, wherein the preset alloy database is usually an alloy database of finite element analysis software QSORM, and the alloy database can be a Hansel-Spittel model specifically, and the standard thermal deformation constitutive model comprises standard material parameters. Suppose the target profile is an alloy cast bar of the composition shown in table 1.

TABLE 1 target section bar main alloy element content (mass ratio,%)

Standard material parameters in the constitutive model due to standard thermal deformation are set based on national standard components. The target profile belongs to specific alloy components, so that the thermal deformation constitutive equation can only correct the model of the original system after recalculation through a thermal compression simulation experiment. However, most users of QFORM or other finite element software only use the model of the system, and the influence of specific alloy components on the accuracy of the model is not considered, so that the simulation calculation result is greatly different from the actual calculation result.

The warm compression experiments can be performed on a Gleeble-3500 model thermal simulation tester. By performing thermal compression experiments at different test temperatures and test strain parameters, including test strain force, test strain amount and test strain rate, and recording corresponding mechanical behavior data, the stress-strain curve of the target profile under different deformation conditions can be obtained. These experimental data can be used to verify and adjust the thermally deformable constitutive model used in the finite element simulation to ensure accuracy of the simulation results. The expression of the thermal deformation constitutive model of the target profile is as follows:

wherein:indicating test strain force, +.>Indicating the test strain capacity, +.>Indicating the test strain rate, +.>Indicating the test temperature +.>Are different optimal material parameters.

The model optimization and adjustment process specifically comprises the steps of calculating all test results by adopting a linear fitting method to obtain optimal material parameters, and replacing the standard material parameters in the standard thermal deformation constitutive model with the optimal material parameters to obtain the thermal deformation constitutive model of the target section bar. The parameter correction specific values are shown in table 2.

Table 2 material parameter correction

Average Absolute Relative Error (AARE) was used to further evaluate the accuracy of the thermally deformed constitutive model of the target profile. By calculation, the AARE value is 4.93%, which shows that the proposed thermal deformation constitutive model and the optimal material constant can well describe the relation between the flow stress, temperature, strain rate and strain of the target profile.

In one embodiment, the step S103 specifically includes the following steps:

arranging a plurality of first measuring points along the length direction of the target die at the cavity part;

a plurality of second measuring points are arranged on the thick-wall part around the geometric center of the thick-wall part;

performing finite element simulation on the profile molding of the target die according to the thermal deformation constitutive model;

detecting fluid flow rates of a plurality of first measuring points in a section molding finite element simulation process, and calculating a flow rate standard deviation based on all the fluid flow rates to obtain an optimized variable index of a target die;

detecting fluid pressure of a plurality of first measuring points in a section molding finite element simulation process, and calculating pressure standard deviation based on all the fluid pressure to obtain a pressure standard deviation as an optimization variable index;

detecting fluid pressure of a plurality of second measuring points in the finite element simulation process of profile molding, and calculating to obtain thick-wall hydrostatic pressure based on all the fluid pressure as an optimization variable index;

and determining optimization targets of the standard deviation of the flow speed, the standard deviation of the pressure and the hydrostatic pressure of the thick wall by combining the molding change of the profile in the process of multiple-profile molding finite element simulation.

In this embodiment, QSORM software may be used to perform station setup and profile modeling finite element simulation. And reading the hydrostatic pressure at all the second measuring points through QFOrm software, wherein the thick-wall hydrostatic pressure is the average value of the hydrostatic pressures at all the second measuring points. The flow standard deviation is the flow velocity variance of the fluid at all the first measuring points, namely the section flow velocity variance of the target profile, and the flow standard deviation has the following calculation formula:

Wherein:represents the standard deviation of the flow rate, +.>The number of measuring points representing the first measuring point, +.>Indicate->Fluid flow at the first measuring point, +.>The average of the fluid flow rates at all the first stations is shown.

The standard deviation of the pressure is the fluid pressure variance of all the first measuring points, and the calculation formula of the standard deviation of the pressure is as follows:

wherein:represents the standard deviation of the pressure>Indicate->Fluid pressure at the first measuring point, +.>The average of the fluid pressure at all the first stations is shown.

In combination with modeling of the modeling variation of the profile in the multiple profile modeling finite element modeling process, the optimization objective of the flow standard deviation should be to minimize the flow standard deviation in order to ensure the profile discharge equalization optimization. In order to ensure that the mold core is stable and does not deform, the dimensional accuracy of the profile and the service life of the mold are optimized, and the optimization target of the pressure standard deviation is to minimize the pressure standard deviation. In order to ensure that the internal structure of the profile is uniform and deadly quality anomalies such as looseness and hollows do not occur, the optimization target of the thick-wall hydrostatic pressure should be to maximize the thick-wall hydrostatic pressure.

In one embodiment, the mold structure parameters include a dam table height (baffe lands), a working tape length (Bearing), and a False Core height (False Core), and the following steps are specifically included before step S104:

Combining the structural parameters of the die and a plurality of optimized variable indexes, and performing finite element simulation analysis according to the test design of an effect surface method (Box-Behnken) to obtain a plurality of parameter relations between the structural parameters of the die and the optimized variable indexes;

In this embodiment, the effect plane method (Box-Behnken) experiment is a commonly used design experiment method for modeling the relationship between input variables (factors) and output responses. The method is a multi-factor and multi-level design method, and the influence of factors on response can be quickly and effectively determined. And carrying out finite element simulation analysis according to the experimental design of the effect surface method to obtain various parameter relations between the structural parameters of the die and a plurality of optimized variable indexes, as shown in table 3.

TABLE 3 multiple parameter relationships between mold structural parameters and multiple optimization variable indices

According to the data in Table 3, modeling is performed by using a Design-Expert by adopting a stepwise regression method, and three ternary quadratic regression models of three optimized variable indexes of the height (P) of the material blocking table, the length (H) of the working belt, the height (F) of the false core head, the standard deviation of the flow speed, the standard deviation of the pressure and the hydrostatic pressure of the thick wall are respectively obtained.

The ternary quadratic regression model includes a flow rate standard deviation regression model, a pressure standard deviation regression model, and a thick-wall hydrostatic pressure regression model. Wherein, the flow rate standard deviation regression model analysis table is shown in Table 4.

TABLE 4 Standard deviation regression model analysis of flow rates

As can be seen from table 4, the standard deviation regression model of flow rate has a degree of freedom of 7 and the residual degree of freedom of 9. F-value test is performed on regression equation by checking different significance levelsUnder the condition, the F value can be found by looking up a table: />，，/>. The regression model in table 4 has an F value f=56.82 much greater than the respective significance level +.>The following F values illustrate that the relationship between the standard deviation regression model of flow rate and dependent variables is quite significant.

And (3) carrying out P test on each item in the regression equation, wherein the influence of the item with the P less than or equal to 0.05 on the dependent variable is obvious, the influence of the item with the P less than or equal to 0.01 on the dependent variable is extremely obvious, the influence of the item with the P more than 0.5 on the dependent variable is not obvious, and the item is generally removed. After the PF term and the P2 term are recalculated, each P value in the table 4 accords with the judgment of 'extremely remarkable'.

The "R-Squared" value is used to evaluate the fitness of the model, and this value is close to 1, indicating that the model is very interpretable. In order to prevent the model from being excessively fitted, an 'Adj R-Squared' value is introduced, and the value is close to 1, so that the high fitting goodness of the die is further illustrated; the "Pred R-Squared" test calculates the fitting degree of the model predicted value and the actual value, the value is close to 1, and the deviation with the "Adj R-Squared" value is small, which indicates that the model has better prediction capability. The "Adeq Precision" value is used to measure the signal to noise ratio, and values greater than 4 generally prove desirable for the model.

And (3) synthesizing the analysis, and finally obtaining the expression of the flow rate standard deviation regression model as follows:

the model analysis table of the pressure standard deviation regression model is shown in Table 5, and the model analysis table of the thick-wall hydrostatic pressure regression model is shown in Table 6.

TABLE 5 pressure standard deviation regression model analysis

TABLE 6 analysis of thick wall hydrostatic pressure regression model

The analytical steps of table 4 were used to perform the same analysis as those of table 5 and table 6 to obtain the expression of the pressure standard deviation regression model as follows:

/>

the expression of the thick-wall hydrostatic pressure regression model is as follows:

in this embodiment, the step S104 specifically includes the steps of:

Sequentially taking the standard deviation of the flow speed, the standard deviation of the pressure and the hydrostatic pressure of the thick wall as response targets, and taking any two of the structural parameters of the die as influence factors to generate a plurality of second-order response curved surfaces;

analyzing all second-order response curved surfaces to determine the influence relation between the structural parameters of the die and a plurality of optimized variable indexes;

In the present embodiment, referring to fig. 5, a second order response surface is generated with the flow rate standard deviation SDV as a response target and the operating band length (Bearing) and the False Core height (False Core) as influence factors. Fig. 5 shows the effect of interaction between the working band length and the false core height on the standard deviation of flow rate. It can be observed from the figure that as the height of the dummy head increases, the standard deviation of the flow rate decreases, indicating that the increase in the height of the dummy head has a positive effect on the equalization of the profile output. In addition, as the operating band length increases, the flow rate standard deviation tends to decrease and then increase, indicating that there is a particular operating band length such that the flow rate standard deviation is minimized under this interaction condition.

Referring to fig. 6, a second order response surface is generated using the flow rate standard deviation SDV as a response target and using the dam table height (baffe lands) and the False Core height (False Core) as influence factors. Fig. 6 shows the effect of interaction between dam table length and dummy head height on flow rate standard deviation. Under the interaction condition, the increase of the height of the material blocking table can lead to the reduction of the standard deviation of the flow rate, which indicates that the greater the height of the material blocking table is, the better the uniformity of profile discharging is. While as the height of the dummy head increases, the standard deviation of the flow rate tends to decrease and then increase, and the optimization of the standard deviation of the flow rate can be achieved at a particular dummy head height.

The above phenomenon is caused by that the resistance to the position with concentrated mass on the section is smaller in the section forming process, so that the discharging speed of the thick wall is faster than that of the thin wall. The larger the wall thickness difference, the larger the flow velocity difference. To adjust the flow rate, this can be done in two ways. The first way is to increase the resistance at the thick wall, i.e. increase the working belt length or the height of the dam table. Resistance increases by increasing friction and changing the metal flow direction, and as both structural dimensions increase, resistance increases accordingly. However, it should be noted that if the resistance is too high, the metal flow at the thick wall will be excessively inhibited, resulting in an increase in the flow velocity difference across the profile section and thus in the flow velocity standard deviation SDV. The second way is to reduce the amount of metal supplied at this location, which can be achieved by increasing the height of the dummy head. Increasing the height of the dummy head reduces the volume of metal involved in the formation, thereby reducing the flow rate of the metal. However, if the volume of metal involved in molding is too small, abnormal voids may be generated at the corresponding cross-sectional positions of the dummy core head in addition to the excessively slow flow rate. As shown in fig. 5 and 6, in combination with the comparison of the F values in table 4, it is known that the order of the major and minor factors affecting the standard deviation SDV of the flow rate is: p (144.55) > F (107.56) > H (40.24).

Referring to fig. 7, a second order response surface is generated using the pressure standard deviation SDP as a response target and using the dam bar height (baffe lands) and the False Core height (False Core) as influence factors. Referring to fig. 8, a second order response surface is generated with the thick-wall hydrostatic pressure (Hydrostatic Pressure) as a response target and the dam table height (baffe lands) and the False Core height (False Core) as influence factors. As shown in fig. 7 and 8, the increase in dummy head height and the increase in dam table height increases the profile pressure standard deviation SDP and reduces the thick wall hydrostatic pressure. This is because the thick-walled portion is less resistant, resulting in a lower distribution of hydrostatic pressure over the section of the profile, while the dummy head limits the filling space for the metal and the dam table limits the flow of metal to specific areas. These two factors increase the pressure instability of the entire profile section while reducing the thick-wall hydrostatic pressure, resulting in an increase in the standard deviation of pressure.

From the comparison of the values of F in Table 5, it is seen that the primary and secondary factors of the pressure standard deviation SDP are ranked in order of P (404.87) > H (248.47) > F (18.43). As a comparison of the values of F in Table 6, the major and minor factors of the thick-wall hydrostatic pressure were ranked in order of F (798.72) > P (220.87) > H (51.21).

Through the analysis, finally, based on a ternary quadratic regression model and combining an influence relation and an optimization target, a parameter relation model between the structural parameters of the die and a plurality of optimization variable indexes can be simplified into the following expression:

in one embodiment, the step S105 specifically includes the following steps:

performing multi-objective optimization on the parameter relation model by using an NSGA2 algorithm based on the optimization targets to obtain Pareto optimal solution sets of all the optimization targets;

taking all optimization targets as evaluation indexes, and generating an index matrix based on a Pareto optimal solution set;

normalizing the index matrix;

weighting each element in the index matrix by using index weights preset by the evaluation index to obtain a weighting matrix;

based on the weighting matrix, the TOPSIS method is adopted to evaluate and sort the solutions in the Pareto optimal solution set, and finally the optimal final solution which achieves all the optimal targets and belongs to the optimal level in the Pareto optimal solution set is obtained.

In this embodiment, the three optimization variable indexes of the flow rate standard deviation SDV, the pressure standard deviation SDP and the thick-wall hydrostatic pressure have independence and have a certain inherent relationship, and a certain optimization target is found to improve to the maximum extent without sacrificing the optimization targets of any two of the optimization variable indexes, so that the optimization method belongs to the Pareto optimal solution set solving problem, and therefore, the multi-target optimization calculation can be performed by adopting the NSGA2 algorithm. The following concepts exist in the NSGA2 algorithm application process:

1. Dominant (dominate) and non-inferior (non-reference)

In the multi-objective optimization problem, if individual p has at least one objective better than individual q and all objectives of individual p are not worse than individual q, then individual p is said to dominate individual q (p dominates q), or individual q is said to be dominated by individual p (q is dominated by p), so to speak, individual p is not inferior to individual q (pis non-index to q).

2. Sequence value (rank) and front end (front)

If p dominates q, then p has a lower order value than q. If p and q are mutually exclusive or, alternatively, p and q are mutually non-exclusive, then p and q have the same order value. Individuals with a rank value of 1 belong to the first front end, individuals with a rank value of 2 belong to the second front end, and so on. Obviously, in the current population, the first front end is completely non-dominant and the second front end is dominant by the individuals in the first front end. Thus, by sorting, individuals in a population can be separated into different front ends.

3. Crowding distance (crowding distance)

The crowding distance is used to calculate the distance between a certain person in a front end and other persons in the front end, and is used to represent the crowding degree among the persons. Obviously, the larger the value of the crowding distance, the less crowded the individuals are, and the better the diversity of the population is. It should be noted that it is not meaningful that the crowding distance is calculated only between individuals at the same front end and between individuals at different front ends.

Based on an optimization target, performing multi-target optimization on the parameter relation model by using an NSGA2 algorithm, and completing optimization calculation through matlab programming to obtain a Pareto optimal solution set. The Pareto optimal solution set has t solutions, 3 optimization targets are used as evaluation indexes, and an index matrix is generated based on the Pareto optimal solution set：

Wherein:representing Pareto optimal solution set, +.>Representing the optimization objective.

For index matrixNormalization processing is carried out, and the specific formula is as follows:

wherein:normalized matrix element, < >>Representing the largest element in the index matrix, +.>Representing the smallest element in the index matrix.

Then, the index weight preset by the evaluation index is used for giving weight to each element in the index matrix to obtain a weight matrix：

Wherein:、/>、/>all are index weights, and are->、/>、/>And respectively representing Pareto optimal solution sets corresponding to the optimization targets.

And finally, evaluating and sequencing all solutions in the Pareto optimal solution set by adopting a TOPSIS method based on the weighting matrix, and finally obtaining an optimal final solution which achieves all optimization targets in the Pareto optimal solution set and belongs to an optimal level.

In one embodiment, the step of obtaining Pareto optimal solution sets of all optimization targets based on optimization targets and performing multi-target optimization on the parameter relation model by using an NSGA2 algorithm specifically includes the following steps:

Randomly generating an original population based on the parameter relation model;

and performing repeated iterative evolutionary operation on the original population by using an NSGA2 algorithm until the iteration times reach a preset algebraic threshold, wherein the repeated iterative evolutionary operation comprises the following steps of:

calculating the crowding distance of the original population based on the target value, and performing a rapid non-dominant sorting operation on the original population according to the crowding distance to screen out part of individuals in the original population;

performing cross mutation operation on the basic population by combining preset cross probability and preset mutation probability to obtain a new generation population, and combining the new generation population and the original population into the original population for the next iteration evolution;

and taking the target value of each individual in the new generation population of the last round of iterative evolution as a Pareto optimal solution set of all optimization targets.

In this embodiment, for example, referring to fig. 9, assuming that the number of original populations is 100, the crossover probability is 0.8, the mutation probability is 0.1, the algebraic threshold is 100, the above steps are performed by Matlab programming to obtain Pareto optimal solution sets of all optimization targets, as shown in fig. 9, the Pareto optimal solution sets in fig. 9 have 18 optimal solutions.

In one embodiment, the step of evaluating and sorting the solutions in the Pareto optimal solution set based on the weighting matrix and by adopting a TOPSIS method, and finally obtaining an optimal final solution which achieves all the optimization targets and belongs to the optimal level in the Pareto optimal solution set specifically comprises the following steps:

taking the minimum element of each column in the weighting matrix as an optimal solution, and taking the maximum element of each column in the weighting matrix as an worst solution;

and performing descending order sorting on the proximity indexes, and selecting the element at the first position of the sorting order as an optimal final solution which achieves all optimization targets and belongs to the optimal level in the Pareto optimal solution set.

In this embodiment, the minimum element in each column of the weighting matrix is used as an optimal solution, and the expression formula of the optimal solution is as follows:

taking the maximum element in the weighting matrix as the worst solution, and the expression formula of the worst solution is as follows:

calculating each element in weighting matrixEuclidean distance between the best solution and the worst solution + >And->The specific calculation formula is as follows:

respectively calculating the proximity indexes of each element and the optimal level according to Euclidean distanceThe specific calculation formula is as follows:

and finally, sorting 18 optimal solutions in the Pareto optimal solution set in a descending order according to the proximity index to obtain a table 7.

TABLE 7 Pareto optimal solution set ordered in decreasing order of approach index

And selecting the element at the first bit of the ordering order as an optimal final solution which achieves all optimization targets in the Pareto optimal solution set and belongs to the optimal level.

The solution of the number 1 in the table 7 is used as the optimal scheme of the optimal design of the die, and from the practical design and manufacturing consideration, the structural parameters of the final die are confirmed to be 0.0mm in height of the material blocking table, 20.0mm in length of the working belt and 1.5mm in height of the false core head. And establishing a three-dimensional model according to the mould structure parameters of the optimal scheme and the initial scheme, and carrying out simulation comparison on the extrusion process by utilizing QORm. As shown in Table 8, the simulation values of the two schemes are compared with those of the two schemes, and as shown in Table 8, compared with the initial scheme, the speed standard deviation of the optimal scheme is reduced by 5.33%, the pressure standard deviation is reduced by 11.10%, the hydrostatic pressure of the thick wall is increased by 26.47%, the die designed and manufactured according to the optimal scheme can smoothly produce the profile, the quality requirement is met, and the effectiveness of the invention in optimizing the complex multi-cavity profile die is proved.

Table 8 best vs. initial protocol results

The invention also discloses a section mould optimization system based on the multi-objective optimization algorithm, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the section mould optimization method based on the multi-objective optimization algorithm in any one of the embodiments.

The implementation principle of the embodiment is as follows:

the following processes are realized through the calling of the program: determining a plurality of optimization variable indexes and optimization targets of all the optimization variable indexes of the target mold through the finite element simulation of the profile molding, and obtaining a functional relation between the mold structure parameters and the plurality of optimization variable indexes of the target mold through response surface analysis, so as to construct a parameter relation model. Meanwhile, in order to improve the accuracy of the functional relation and the authenticity of the simulation process, the thermal deformation constitutive model of the target profile is considered and optimized. And finally, calculating a parameter relation model of the nonlinear function formula through an NSGA2 multi-objective genetic optimization algorithm to obtain an optimized final solution, optimizing and adjusting the structural parameters of the die through the optimized final solution, and completing die manufacturing according to the optimized result. Because more key mold structural parameters exist in the complex multi-cavity large-wall-thickness profile mold, compared with the process of optimizing the mold by adopting a single optimization target, the multi-target optimization can obtain an optimal combination scheme of the key mold structural parameters, so that the optimized mold can simultaneously meet a plurality of index requirements when being applied to the profile processing process, and the finally processed profile can also meet the quality requirements.

Those of ordinary skill in the art will appreciate that: the discussion of any of the embodiments above is merely exemplary and is not intended to imply that the scope of the present application is limited to such examples; the technical features of the above embodiments or in the different embodiments may also be combined under the idea of the present application, the steps may be implemented in any order, and there are many other variations of the different aspects of one or more embodiments in the present application as above, which are not provided in details for the sake of brevity.

One or more embodiments herein are intended to embrace all such alternatives, modifications and variations that fall within the broad scope of the present application. Any omissions, modifications, equivalents, improvements, and the like, which are within the spirit and principles of the one or more embodiments in the present application, are therefore intended to be included within the scope of the present application.

Claims

1. The section bar die optimization method based on the multi-objective optimization algorithm is characterized by comprising the following steps of:

obtaining a die structure parameter of a target die to be optimized and profile parameters of a target profile produced by using the target die, wherein the target profile comprises a cavity part, a thin-wall part and a thick-wall part, the profile parameters comprise a plurality of groups of test temperature parameters and a plurality of groups of test strain parameters, and the test strain parameters comprise test strain force, test strain quantity and test strain rate;

carrying out multiple hot compression tests by combining multiple groups of test temperature parameters and multiple groups of test strain parameters, and calculating all test results by adopting a linear fitting method to obtain optimal material parameters;

replacing the standard material parameters in the standard thermal deformation constitutive model with the optimal material parameters to obtain a thermal deformation constitutive model of the target profile;

the expression of the thermal deformation constitutive model of the target profile is as follows:

wherein:representing the test strain force,/->Representing the test strain amount,/->Which is indicative of the rate of strain in the test,representing the test temperature parameter,/->、/>For different said optimal material parameters;

2. The method for optimizing a section mold based on a multi-objective optimization algorithm according to claim 1, wherein the step of performing a section molding finite element simulation on the objective mold according to the thermal deformation constitutive model, determining a plurality of optimization variable indexes of the objective mold and optimization targets of the optimization variable indexes, respectively, comprises the steps of:

3. The method for optimizing a profile die based on a multi-objective optimization algorithm according to claim 2, wherein the die structure parameters include a material blocking table height, a working belt length and a false core height, and further comprising the steps of, before the obtaining of the influence relation between the die structure parameters and the plurality of optimized variable indexes by the response surface analysis, constructing a parameter relation model between the die structure parameters and the plurality of optimized variable indexes by combining the influence relation and the optimization objective:

4. A profile die optimization method based on a multi-objective optimization algorithm according to claim 3, wherein the obtaining the influence relation between the die structural parameter and a plurality of the optimization variable indexes through response surface analysis, and constructing a parameter relation model between the die structural parameter and a plurality of the optimization variable indexes by combining the influence relation and the optimization objective, comprises the following steps:

5. The multi-objective optimization algorithm-based profile die optimization method according to claim 1, wherein the multi-objective optimization of the parametric relationship model based on the optimization objective and using a fast non-dominant ordering algorithm with elite retention policy, obtaining an optimized final solution to achieve all the optimization objectives, comprises the steps of:

normalizing the index matrix;

6. The multi-objective optimization algorithm-based profile die optimization method according to claim 5, wherein the multi-objective optimization of the parametric relationship model based on the optimization objective and using a fast non-dominant ordering algorithm with elite retention policy to obtain Pareto optimal solution sets of all the optimization objectives comprises the steps of:

7. The method for optimizing a section bar die based on a multi-objective optimization algorithm according to claim 5, wherein the steps of evaluating and sorting the solutions in the Pareto optimal solution set based on the weighting matrix and using a TOPSIS method, and finally obtaining an optimized final solution in the Pareto optimal solution set, which achieves all the optimization objectives and belongs to an optimal level, comprise the following steps:

8. A multi-objective optimization algorithm based profile die optimization system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the multi-objective optimization algorithm based profile die optimization method according to any one of claims 1 to 7 when executing the computer program.